Liquid behavior of cross-linked actin bundlesKimberly L. Weiricha, Shiladitya Banerjeea,b,c, Kinjal Dasbiswasa, Thomas A. Wittena,d,Suriyanarayanan Vaikuntanathana,e, and Margaret L. Gardela,d,f,1

aJames Franck Institute, University of Chicago, Chicago, IL 60637; bDepartment of Physics and Astronomy, University College London, London WC1E 6BT,United Kingdom; cInstitute for the Physics of Living Systems, University College London, London WC1E 6BT, United Kingdom; dDepartment of Physics,University of Chicago, Chicago, IL 60637; eDepartment of Chemistry, University of Chicago, Chicago, IL 60637; and fInstitute for Biophysical Dynamics,University of Chicago, Chicago, IL 60637

Edited by David A. Weitz, Harvard University, Cambridge, MA, and approved January 10, 2017 (received for review September 28, 2016)

The actin cytoskeleton is a critical regulator of cytoplasmic architec-ture and mechanics, essential in a myriad of physiological processes.Herewe demonstrate a liquid phase of actin filaments in the presenceof the physiological cross-linker, filamin. Filamin condenses shortactin filaments into spindle-shaped droplets, or tactoids, withshape dynamics consistent with a continuum model of anisotropicliquids. We find that cross-linker density controls the dropletshape and deformation timescales, consistent with a variableinterfacial tension and viscosity. Near the liquid–solid transition,cross-linked actin bundles show behaviors reminiscent of fluidthreads, including capillary instabilities and contraction. Thesedata reveal a liquid droplet phase of actin, demixed from the sur-rounding solution and dominated by interfacial tension. These re-sults suggest a mechanism to control organization, morphology,and dynamics of the actin cytoskeleton.

actin | phase separation | liquid crystal | cytoskeleton

The cellular cytoplasm is a hierarchical array of diverse, softmaterials assembled from biological molecules that work in

concert to support cell physiology (1). The actin cytoskeletonconstitutes a spectrum of materials constructed from the semi-flexible polymer actin (F-actin) that are crucial in diverse phys-ical processes ranging from cell division and migration to tissuemorphogenesis (2, 3). Cross-linking and regulatory proteins as-semble actin filaments into bundles and networks with variedcomposition, mechanics, and physiological function (4). Themechanical properties of actin assemblies regulate force gener-ation and transmission to dynamically control morphogenicprocesses from the subcellular to tissue length scales (5, 6).A mechanistic understanding of cytoplasmic mechanics is

obscured by the rich complexity of in vivo cytoskeletal assemblies(7) and has been investigated via in vitro model systems (8, 9).Vastly different material properties have been accessed throughvarying filament length, concentration, and cross-linking. For sem-idilute concentrations of long actin filaments (>1 μm), the meanspacing between actin filaments, or mesh size, is much smaller thanthe filament length. In this case, cross-linking proteins mechanicallyconstrain actin filaments to result in space-spanning networksthat are viscoelastic gels (10). The structure of cross-linked actinnetworks is kinetically determined, reflecting a metastable state(11, 12) that requires motor-driven stresses for significant shapechanges (13). In contrast, highly concentrated solutions of shortactin filaments (<1 μm) align due to entropic effects and formequilibrium liquid crystal phases (14). Liquid crystal theory hasbeen introduced as a framework to understand actin cortexmechanics and mitotic spindle shape (5, 15), but the existence ofliquid crystal-like phases at physiological conditions is uncertain.Liquid-like phases of proteins and nucleic acids have been

found within the cytoplasm and are thought to be important insubcellular organization (16). Weak and transient interactionstrigger these biomolecules to phase separate from the cytoplasminto droplets, with shape and dynamics dominated by interfacialtension and viscosity (16). Here we demonstrate liquid dropletscomprised of cross-linked, short actin filaments. We focus ondilute actin concentrations where cross-linkers are critical to

induce phase separation of actin into droplets with tunable tac-toid shape. Consistent with a liquid composed of rods, we candescribe the droplet shape and dynamics with an anisotropicliquid continuum model. Finally, we demonstrate actin bundlesthat exhibit shape changes reminiscent of fluid threads, withinterfacial tension driven pearling and shortening. This reveals aliquid droplet phase of actin, demixed from the surroundingsolution, with shape dominated by interfacial tension.

ResultsLiquid Droplets Formed by Short Actin Filaments Cross-Linked byFilamin. We polymerize actin filaments beginning with a dilute(2.6 μM) suspension of actin monomers in the presence of cap-ping protein, which limits filament growth (17). Under theseconditions, the average distance between filaments, or mesh size,is ∼1 μm (18) and much larger than the average F-actin length,∼180 nm, such that filaments freely diffuse and form a uniform,isotropic mixture (Fig. 1A, Left; SI Text; and Movie S1). Adding0.26 μM of the F-actin cross-linker filamin (19) triggers suddendensity changes in the mixture. Actin filaments rapidly assembleinto spindle-shaped aggregates of high density, estimated to be250-μM monomeric actin; a negligible density of filaments re-main in the bulk (Fig. 1B, Left). The tactoids grow over time,increasing in length from ∼1 to 4 μm during the first 60 min afterfilamin addition (Fig. 1A and Movie S1).These aggregates have a characteristic spindle shape, mathe-

matically described as a tactoid, which is a signature shape ofliquid crystal droplets (20). Liquid crystal phases form in highly

Significance

The interior of biological cells is composed of soft, macromo-lecular-based materials. The semiflexible biopolymer actincross-links into networks and bundles with diverse architec-tures to form the actin cytoskeleton. Actin networks have beentraditionally thought to be viscoelastic gels, whose rigiditycontrols cell morphogenesis. Here we demonstrate that cross-linked actin filaments also form liquid droplets. Because theseliquids are composed of rod-like polymers, they form aniso-tropic liquid droplets with a spindle-like shape, whose mor-phology can be controlled by cross-link concentration. Actin-based liquid bundles also display shape instabilities character-istic of fluids. These shape dynamics reveal a mechanism tocontrol subcellular compartmentalization and dynamics, withimplications for mitotic spindle shape and molecular motor-independent contractility.

Author contributions: K.L.W., S.B., S.V., and M.L.G. designed research; K.L.W. performedexperiments; S.B. and K.D. developed the model; K.L.W., S.B., K.D., T.A.W., S.V., andM.L.G. contributed new reagents/analytic tools; K.L.W., S.B., and K.D. analyzed data;and K.L.W., S.B., K.D., S.V., and M.L.G. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.1To whom correspondence should be addressed. Email: gardel@uchicago.edu.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1616133114/-/DCSupplemental.

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concentrated suspensions of rods where entropic effects drivethe nucleation of orientationally ordered droplets within a denseisotropic background (Fig. 1B, Right) (21, 22). For actin fila-ments of the length in our experiments, these phases occur atconcentrations of ∼250 μM (23) (SI Text). Here we find thatfilamin induces the formation of tactoids at 100-fold lower actinconcentration. In further contrast to traditional liquid crystaltactoids, cross-linked tactoids are surrounded by an undetectablylow concentration of F-actin (Fig. 1B, Left).To probe whether cross-linked actin tactoids are fluid, we in-

vestigate the actin filament mobility via fluorescence recoveryafter photobleaching (Fig. 1C, images, and Movie S2). Afterphotobleaching a region of the tactoid, the F-actin fluorescenceintensity recovers in the bleached region, suggesting that fila-ments rearrange within the tactoid (Fig. 1C and Fig. S1). Wequantify the recovery by plotting the ratio of the fluorescenceintensity on the bleached side to the unbleached side as a

function of time. The increasing intensity ratio with time is fit toa rising exponential, yielding a recovery time of τR ∼ 900 s. Fromthis, we estimate a diffusion coefficient of D ∼ 0.3 × 10−2 μm2/sand a viscosity, η ∼ 3 Pa·s (SI Text), comparable to viscositiesreported in other protein and colloid systems (24).We observe tactoids over a range of actin filament lengths

(0.1–1 μm) and filamin concentrations (1–10 mol %) (Fig. 1D).At longer filament lengths, we observe the formation of space-spanning actin networks, which have a viscoelasticity that hasbeen well studied (25). At extremely low filament lengths orcross-link concentrations, tactoids do not form, and actin fila-ments freely diffuse in solution, analogous to a gas phase.

Tactoid Shape Can Be Modulated by Filament Cross-Linking. Thus far,we have only observed tactoid formation with filamin. Cross-links are typically thought of as interacting with the filaments inan anisotropic fashion, by promoting actin filament alignment.

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Fig. 1. Liquid droplets of cross-linked and short F-actin. (A) Fluorescence images of tetramethylrhodamine-labeled actin (TMR-actin) (1 mol % cappingprotein) before (actin only) and after addition of 10 mol % filamin (added at t = 0). (B) Tactoids are the shape of entropically formed liquid crystal dropletsnear the isotropic–nematic phase transition (Right). Here we observe tactoids induced by the addition of cross-linkers (Left). (C) Images of TMR-actin within atactoid (1.5 mol % capping protein and 5 mol % filamin; Upper), with photobleaching occurring at t = 0 min. Average normalized TMR-actin intensity of thephotobleached region over time (dashed line indicates exponential fit with τR = 880 s). (D) Phase diagram of solid, liquid, and gas phases of cross-linked actin.Black plus symbols are data where dispersed filaments are observed, blue filled circles are samples exhibiting tactoid droplets, dark blue open circles aresamples with fluid bundles (Fig. 4), and black crosses are samples where space spanning networks are observed.

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However, filamin is a long (∼150 nm) and flexible actin cross-linker, with transient binding kinetics (19). This may allow for aless orientationally constrained, long-range attractive interactionbetween filaments. Thus, cross-links may serve as a source of

isotropic or anisotropic cohesion between filaments. To explorethis, we form tactoids with variable filamin concentration from2.5 to 15 mol % (Fig. 2A, images and open circles). We describethe resulting tactoid shape by the aspect ratio, L/r, where L and rare the major and minor axes lengths, respectively. At low fila-min concentration, tactoids are elongated (L/r ∼ 3 for 2.5 mol %filamin). Strikingly, we find that as the concentration of filamincross-links increases, the tactoid aspect ratio decreases (L/r ∼ 2for 15 mol % filamin).To understand tactoid shape, we model the tactoid as a fluid

droplet using a continuum theory (SI Text). An ordinary liquiddroplet has purely isotropic interfacial tension, and the optimalequilibrium shape is a sphere (Fig. 2B). In contrast, a liquidcrystal droplet is made of anisotropic particles, which gives riseto an anisotropic interfacial tension (21). A collection of rodswith purely anisotropic interactions would have a preferredequilibrium shape of a cylinder (Fig. 2B), with a tendency ofrod-like particles to align with the interface. Thus, we model atactoid as a droplet with both isotropic, γI, and anisotropic, γA,interfacial tension components (20, 21) (SI Text and Fig. S2).The optimal shape of the droplet is determined by minimizingthe interfacial energy, controlled by a single dimensionlessparameter, ω = γA/γI. The balance of anisotropic and isotropicinterfacial tensions yields elongated shapes for ω > 0, whichbecome increasingly elongated as ω grows and sharp featuresemerge for ω > 1 (Fig. 2C).We calculate ω from the experimentally observed aspect ratios

using the theoretical relation L=r= 2ω1 =

2 for ω≥ 1 (20) (SI Text).We observe that ω is inversely proportional to filamin concen-tration (Fig. 2A, diamonds). Thus, filamin alters ω such that therelative contribution of isotropic interfacial tension increaseswith respect to the anisotropic interfacial tension. This indicatesthat filamin serves primarily as cohesion between F-actin, ratherthan to enforce F-actin alignment within droplets.

Cross-Link Concentration Modulates Tactoid Shape Dynamics. Over100 min, the average tactoid length increases as a power law,L  ∼ tα, where α = 0.47 ± 0.01 (Fig. 3A, dashed, and Movie S3).Notably, as the average size increases, the tactoid aspect ratioremains constant (Fig. 3A, open squares). This is consistent withtheory and experiments on tactoids with homogeneous nematicalignment (26, 27) (SI Text).Tactoid growth likely occurs via coarsening mechanisms as-

sociated with conventional liquid droplets, including Ostwaldripening and droplet coalescence (28). At the earliest observedstages of tactoid formation, there is a negligible concentration ofF-actin in the bulk. This suggests that tactoid growth via singlefilament accretion, or Ostwald ripening, is unlikely. Instead, weobserve individual coalescence events where two initially sepa-rate tactoids merge into a single elongated droplet that relaxes,within minutes, into a larger tactoid (Fig. 3B, images, and MovieS4). Moreover, the scaling exponent we measure in growth dy-namics is consistent with that expected for coarsening of iso-tropic liquid droplets via interfacial tension-driven coalescence(α = 0.5) (28).As a further test that liquid properties dominate tactoid

growth via coalescence, we probe the droplet deformation dy-namics. We measure the tactoid length, L, along the major axis,over time as two initially separate tactoids coalesce (Fig. 3B).After initial coalescence (L = Li), the length rapidly decreases asthe merged droplet shape relaxes toward a steady-state tactoidshape with L = Lf. The length shortening is consistent with anexponential decay from which we extract a single characteristicrelaxation time, τ, using L(t) = Lf + (Li − Lf)exp(−t/τ), where τ isa characteristic relaxation time (Fig. 3B, line). Data from mul-tiple coalescence events collapse onto a single master curve uponrescaling the length by the deformation length, Li − Lf, and timeby τ (Fig. 3C).

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Fig. 2. Cross-linking regulates tactoid interfacial tension. (A) Tactoid(1.5 mol % capping protein) images, visualized with TMR-actin for filaminconcentration from 2.5 to 15 mol %. Aspect ratio (black open circles) andratio of anisotropic to isotropic interfacial tension, γA/γI (green diamonds), asa function of filamin concentration. (B) An arbitrary shaped liquid dropletwith purely isotropic interfacial tension relaxes to an equilibrium shape of asphere, whereas a droplet with purely anisotropic interfacial tension relaxesto an elongated, cylindrical equilibrium shape. (C) Model predictions ofliquid droplet shape for varying isotropic and anisotropic interfacial tensionratios.

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Using our continuum model for anisotropic fluids (SI Text), wecan determine the tactoid shape dynamics during coalescence asfunction of γI, γA, and η and extract the characteristic shape re-laxation timescale τ (SI Text). From the model, we calculate τ as afunction of η/γI for varying values of ω= γA/γI (Fig. 3D, dashedlines). We find that τ obtained from experimental data for 5 and10 mol % filamin is consistent with those predicted for ω = 2 and1.4 (values corresponding to those in Fig. 2A), respectively (Fig.3D, symbols). Thus, the shape dynamics during droplet co-alescence events can be quantitatively described with a contin-uum fluid model containing both isotropic and anisotropicinterfacial tensions. From the η/γI obtained in the fit (Table S1),and the viscosity estimated from photobleaching, we estimateγI ∼ 300 nN/m. This interfacial tension is ∼10 times less thanreported for other protein-based liquid droplets (24, 29) butconsistent with theoretical predictions for larger particles such asactin filaments (21). Consistent with coalescence in isotropicdroplets, we observe a linear scaling when we plot the relaxationtime, τ, as a function of the deformation length, Li − Lf, from the

exponential fits (Fig. 3C, Inset). The slope of the line is η/γeff,where γeff is an effective interfacial tension with contributionsfrom both γI and γA (SI Text). The data from the two differentfilamin concentrations fall on the same line, suggesting thatthat cross-link density modifies viscosity and the effective in-terfacial tension proportionally. Together, the droplet shapeand dynamics demonstrate that filamin cross-link concentra-tion modulates both the interfacial tensions and the viscosity ofF-actin droplets.

Interfacial Tension Drives Pearling and Contraction of Bundles. Actinbundles formed with passive cross-linkers are typically thought tobe kinetically trapped structures with few structural rearrange-ments at long times (12). However, our findings suggest thatwhen the actin filaments are sufficiently short, we may be able toobserve bundles displaying fluid-like behavior. We explore this inour system by constructing bundles near the liquid–solid boundary(Fig. 1D). We increased the actin filament length such that theinitial assembly conditions create long (>50 μm), thin (radius

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Fig. 3. Cross-link density regulates interfacial tension and viscosity. (A) Fluorescence images of tactoid growth (1.5 mol % capping protein and 5 mol %filamin), visualized by TMR-actin. Average tactoid length (black closed circles) and aspect ratio (open squares) are shown as a function of time after filaminaddition, and dashed line indicates a power law fit L ∼ t α, where α = 0.47 ± 0.01 for four datasets. Error bars represent ±1 SD. (B) Fluorescence images oftactoids (1 mol % capping protein and 10 mol % filamin) coalescence. Tactoid length, along the major axis, is shown as a function of time as two initially separatetactoids coalesce. Dashed line is an exponential fit. (C) Tactoid length, rescaled by the deformation length, as a function of time, rescaled by the characteristic re-laxation time, for 14 coalescence events (1 mol % capping protein and 5 and 10 mol % filamin) collapses into a master curve. The solid line represents an exponentialdecay. (Inset) Linear scaling between relaxation time and deformation length from exponential fits of length relaxation. (D) The interfacial tension to viscosity ratioobtained from continuum model fits to the experimental data falls on the theoretically predicted curve for anisotropic droplets.

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∼200 nm) bundles of cross-linked F-actin within ∼1 min (Fig. 4 Aand B). After rapid assembly, these bundles continue to changeshape over ∼10 min timescales. Some bundles develop pearlinginstabilities along their length that evolve into periodicallyspaced bulges, which grow circumferentially in time (Fig. 4A andMovie S5). Such behavior is characteristic of a Rayleigh–Plateauinstability observed in fluid columns, where interfacial tensiondrives the growth of periodic bulges that arise from fluctuations(SI Text and Fig. S3). In contrast to simple fluids, where capillaryinstabilities result in droplet breakup (30), we observe instabil-ities that evolve into chains of tactoids bridged by thin bundles.This is reminiscent of polymer fluids, where droplet breakup isarrested by polymer entanglements in the thinning bridges (31)(SI Text). The characteristic length scale of pearling is longerthan that expected from a simple fluid, consistent with our the-oretical model based on anisotropic interfacial tension (SI Text).We also observe bundles that contract (Fig. 4B and Movies S6

and S7). The bundle length, L(t) shortens exponentially in time,reducing in length by 20–60% over ∼10 min (Fig. 4C) toward atactoid shape. This length contraction is captured by our dynamiccontinuum model of a droplet relaxing to its equilibrium shape(SI Text and Fig. 4C). Upon rescaling L(t) by deformation length,Li − Lf, and time by the relaxation time, τ, we find that bundlesacross a range of cross-linking concentrations collapse onto a

single exponential decay (Fig. 4D). This suggests that contractingbundles are also liquid columns that relax to their equilibriumshapes with a characteristic timescale. We find that the extent ofcross-linking provides a tunable parameter to modulate bundlecontractile strain and strain rates (Fig. 4E). Thus, if cross-linkedF-actin bundles are fluidized, interfacial tension is sufficient todrive their contractility.

DiscussionThe experimental characterization of cytoskeletal liquid crystalphases is a nascent field (15, 23, 32, 33). Here we describe aliquid crystal droplet, induced by the addition of cross-links andphase separated from a dilute suspension of anisotropic parti-cles. We find that the physiological cross-linker filamin cross-links short F-actin into liquid crystalline droplets at concentra-tions 100-fold less than the critical concentration expected forentropic ordering. In this unusual, cross-linked liquid crystal,cross-linkers provide attractive interactions, allowing for themodulation of liquid properties such as interfacial tension andviscosity. The liquid phase is likely supported by filamin’s bio-physical properties: filamin is a long (∼150 nm) and flexible actincross-linker, with transient binding kinetics (19). We hypothesizethat these cross-link properties are crucial to allowing filamentorientational and translational mobility to support a liquid

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phase. Understanding the molecular mechanisms to controlmacromolecular liquid phases is an exciting avenue of futureresearch.Evidence of liquid phases of cross-linked biopolymers in vitro

potentially has significant implications for cytoskeletal architec-ture and mechanics. Liquid crystal physics has been invoked todescribe the meiotic spindle shape (15) and actomyosin flows (5).Cross-linked biopolymer tactoids provide a minimal model sys-tem to explore biopolymer liquid crystals. Our data provide ev-idence for a liquid crystal description of spindle shape (15, 34,35), physical properties (15), and scaling with system size (36).These results suggest that liquid crystal theory has the potentialto describe diverse biopolymer assemblies beyond the actin andmicrotubule cytoskeleton, including amyloid fibrils, intermediatefilaments, and bacterial homologs of actin and microtubules.Transitions between solid and liquid phases change the un-

derlying physical properties of materials. Regulatory proteinsin vivo provide dynamic control of biopolymer filament lengthand cross-link affinity, which could potentially drive the system

between a gel and liquid phase to alter bundle mechanics andshape. Most notably, we find that bundles of fluid cross-linkedfilaments relax their shape by contracting, without requiringmolecular motor activity. These results demonstrate that in-terfacial tension is sufficient to drive shortening and shape in-stabilities of bundles, suggesting a mechanism for previouslyreported motor-independent contraction in cells (37). Futureresearch will elucidate the extent to which liquid phases of bio-polymer filaments organize the interior of living cells and howsuch biological structures can inform novel soft materials design.

ACKNOWLEDGMENTS. We acknowledge T. Thoresen and S. Stam for puri-fied filamin and C. Suarez and D. R. Kovar for capping protein. This researchwas supported by the University of Chicago Materials Research Science andEngineering Center (National Science Foundation Division of Materials Re-search Grant 1420709). M.L.G. acknowledges support from National ScienceFoundation Molecular Cellular Biosciences Grant 1344203. S.B. acknowl-edges support from the Institute for the Physics of Living Systems at Univer-sity College London. S.V. acknowledges support from the Universityof Chicago.

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